分形布朗曲面构造算法研究

Research on Algorithm of Fractal Brown Surface Construction

分形布朗运动是描述自然景物分形特征最有效的数学模型之一.以分形布朗运动为基础来构造分形图像可以较好地体现出具有复杂特征的自然景物的特点.提出了一种修正方差的随机中点继承增加算法,并使用该方法进行了模拟.模拟结果表明该算法能够较精确地生成FBM图像.与随机中点位移算法相比,修正方差的随机中点继承增加算法只增加了有限的偏移计算即可达到较高的精度,是一种有效地分形图形生成算法.

The fractal Brownian motion （FBM） is one of the most effective mathematics models for describing fractal features of natural scenery. Based on the fractal Brownian motion, to construct a fractal image can better incarnate the features of complex characters of the natural scenery. The variance corrected successive random additions algorithm （CSRA） is pro- posed and used to simulate in this paper. The result of the simulation shows that the algorithm can generate the FBM image considerably precise. Compared with the algorithm of random midpoint displacement, the algorithm of CSRA can achieve higher precision, only adding limited biased calculation. So the algorithm of CSRA is an effective algorithm to generate fractal graphic.